Theories of strain analysis from shape fabrics: A perspective using hyperbolic geometry

摘要: Abstract A parameter space is proposed for unifying the theories of two-dimensional strain analysis, where markers are approximated by ellipses with a prescribed area. It shown that unified hyperbolic geometry, oldest and simple non-Euclidean geometry. The hyperboloid model geometry used this purpose. Ellipses normalized their areas represented points on unit hyperboloid, curved surface in space. Dissimilarity between defined distance represent ellipses. merit introducing comes from fact equals doubled natural needed to transform one ellipse another. Thus, introduction convenient error analyses. Equal-area gnomonic projections introduced R f / ϕ kinematic vorticity analyses, respectively. In our formulation, optimal set data obtained as centroid corresponding dispersion shows uncertainty strain. By means bootstrap method, confidence region drawn upon surface, equal-area projection Euclidean plane size region. addition, formulation provides new graphical technique analysis using projection. yields number its uncertainty.